Display posts from category in post content?

You can do this with a query

<ul>
<?php
global $post;
$args = array( 'posts_per_page' => 5, 'offset'=> 1, 'category' => 1 );
$myposts = get_posts( $args );
foreach( $myposts as $post ) :  setup_postdata($post); ?>
    <li><a href="https://wordpress.stackexchange.com/questions/6376/<?php the_permalink(); ?>"><?php the_title(); ?></a></li>
<?php endforeach; ?>
</ul>

source

You can put that in your category page or in something like Exec-PHP plugin

For looking up the current category you can grab it like

get_query_var('cat')